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Operating room scheduling under waiting time constraints: the Chilean GES plan

  • S.I.: CLAIO 2016
  • Published:
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Abstract

In 2000, Chile introduced profound health reforms to achieve a more equitable and fairer system (GES plan). The reforms established a maximum waiting time between diagnosis and treatment for a set of diseases, described as an opportunity guarantee within the reform. If the maximum waiting time is exceeded, the patient is referred to another (private) facility and receives a voucher to cover the additional expenses. This voucher is paid by the health provider that had to do the procedure, which generally is a public hospital. In general, this reform has improved the service for patients with GES pathologies at the expense of patients with non-GES pathologies. These new conditions create a complicated planning scenario for hospitals, in which the hospital’s OR Manager must balance the fulfillment of these opportunity guarantees and the timely service of patients not covered by the guarantee. With the collaboration of the Instituto de Neurocirugía, in Santiago, Chile, we developed a mathematical model based on stochastic dynamic programming to schedule surgeries in order to minimize the cost of referrals to the private sector. Given the large size of the state space, we developed an heuristic to compute good solutions in reasonable time and analyzed its performance. Our experimental results, with both simulated and real data, show that our algorithm performs close to optimum and improves upon the current practice. When we compared the results of our heuristic against those obtained by the hospital’s OR manager in a simulation setting with real data, we reduced the overtime from occurring 21% of the time to zero, and the non-GES average waiting list’s length from 71 to 58 patients, without worsening the average throughput.

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Acknowledgements

This work was partially funded by Anillo Project 1407 and Ingeniería 2030, Corfo.

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Correspondence to Susana Mondschein.

Appendices

Data analysis 2015–2016

1.1 Pathologies characterization

In the following section, we report the analysis performed for the case study in Sect. 7. Tables 5, 6, and 7 show the arrival rates per pathology, surgery times, and GES parameters, respectively.

Table 5 Arrival rates (*GES pathology)
Table 6 GES pathology parameters
Table 7 Average surgery time per physician (h)

1.2 Waiting list characterization

Figure 4a, b show the number of patients in each waiting time range at the beginning of the planning horizon for each GES diagnosis. Table 8 contains the number of non-GES patients on the waiting list at the beginning of the planning horizon.

Fig. 4
figure 4

Waiting list characterization. a Waiting time histogram in days for HNP. b Waiting time histogram in days for TU-ENC

Table 8 Number of non-GES patients on the waiting list

Experimental results details

1.1 Simulation based performance analysis

Tables 9 and 10 show the results of the simulations conducted to investigate the effect of due date changes. The simulations were performed using real values for \(C_A\), \(C_B\), \(g_A\), and \(g_B\) and assuming that all physicians can operate on all pathologies. For each case, we simulated 10 years of 30 weeks each and computed the average values for each important metric while scaling \(g_A\) in Table 9 and scaling \(g_B\) in Table 10.

Table 9 Results for changing \(g_A\)
Table 10 Results for changing \(g_B\)

1.2 Performance validation

Tables 11 and 12 show additional details of the case study conducted at Instituto de Neurocirugía to validate the simulation results.

Table 11 OR Manager performance with assigned patient–physician pairs
Table 12 GES-PROG performance with assigned patient–physician pairs

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Barrera, J., Carrasco, R.A., Mondschein, S. et al. Operating room scheduling under waiting time constraints: the Chilean GES plan. Ann Oper Res 286, 501–527 (2020). https://doi.org/10.1007/s10479-018-3008-7

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